Cohomological rigidity for Fano Bott manifolds

Abstract

In the present paper, we characterize Fano Bott manifolds up to diffeomorphism in terms of three operations on matrix. More precisely, we prove that given two Fano Bott manifolds $X$ and $X^{\prime }$, the following conditions are equivalent: (1) the upper triangular matrix associated to $X$ can be transformed into that of $X^{\prime }$ by those three operations; (2) $X$ and $X^{\prime }$ are diffeomorphic; (3) the integral cohomology rings of $X$ and $X^{\prime }$ are isomorphic as graded rings. As a consequence, we affirmatively answer the cohomological rigidity problem for Fano Bott manifolds.

21 pages, 4 figures

References in corpus (2)

• An algorithm for the classification of smooth Fano polytopes
• Cohomological rigidity for toric Fano manifolds of small dimensions or large Picard numbers

Cited by in corpus (1)

• On the enumeration of Fano Bott manifolds